# How does one use NSum within NIntegrate properly?

If I use symbolic integration for the following:

Sum[Integrate[i + x, {x, 1, 7}], {i, 1, 7}]


336

as one can see it gives the answer as it seems to 'understand' the sum integral.

However with

NSum[NIntegrate[i + x, {x, 1, 7}], {i, 1, 7}]


NIntegrate::inumr: The integrand i+x has evaluated to non-numerical values for all sampling points in the region with boundaries {{1,7}}.

336.

As one can see it does not seem to know that $$i$$ is 1 I think or something like that.

What is the problem and how can I format the numerical functions to do what I want without these errors?

• FWIW: Sum[NIntegrate[...]] works just fine. Jun 24, 2019 at 13:28
• Use Quiet[] or ignore it. NSum[] is evaluating its argument symbolically probably to see if it can be differentiated Jun 24, 2019 at 22:09
• Possible duplicate: mathematica.stackexchange.com/questions/18393/… Feb 7, 2021 at 2:57
• Michael E2 Jun 24 '19 at 22:09 then Michael E2 yesterday Feb 07 '21 just noticed aye! Feb 8, 2021 at 12:58

Define a function that can only be called with a numerical argument $$i$$:
f[i_?NumericQ] := NIntegrate[i + x, {x, 1, 7}]

NSum[f[i], {i, 1, 7}]